Approximation of centroid end-points and switch points for replacing type reduction algorithms

Abstract

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik–Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process. • A framework is proposed to mitigate speed and accuracy issue in IT2FLS TR operation. • Proposed framework is application specific and requires tuning for each application. • Proposed framework is data driven and polynomial regression based. • MAPE as low as 0.4% can be achieved in centroid end-point approximation. • Switch point prediction accuracy can be as high as 100%.